The function C(x)=−20x+1681 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $21?

The least number of items to produce is 41

Step-by-step explanation:

Average Cost

Given C(x) as the cost function to produce x items. The average cost is:

The cost function is:

And the average cost function is:

We are required to find the least number of items that can be produced so the average cost is less or equal to $21.

We set the inequality:

Multiplying by x:

Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.

Adding 20x:

Swapping sides and changing the sign:

Dividing by 41:

The least number of items to produce is 41

x = 12

y = 15

step-by-step explanation: